Question

The table below shows the height (in inches) and weight (in pounds) of eight basketball players.

Height

67

69

70

72

74

74

78

79

Weight

183

201

206

220

226

240

253

255

About how many pounds would you expect a basketball player to weigh if his height is 84 inches? Find a line of best fit for this data and use it to make your prediction.

(1 point)
Responses

276.1 lb

289.3 lb

298.4 lb

307.7 lb

Answer 1

To find the line of best fit and make a prediction, we can use linear regression.

First, we need to calculate the slope (m) and y-intercept (b) of the line:

m = ∑((x - mean(x))(y - mean(y))) / ∑((x - mean(x))^2)
b = mean(y) - m * mean(x)

Where:
x = height
y = weight

Using the given data:

x = [67, 69, 70, 72, 74, 74, 78, 79]
y = [183, 201, 206, 220, 226, 240, 253, 255]

mean(x) = (67 + 69 + 70 + 72 + 74 + 74 + 78 + 79) / 8 = 72
mean(y) = (183 + 201 + 206 + 220 + 226 + 240 + 253 + 255) / 8 = 224.375

Σ((x - mean(x))(y - mean(y))) = [(67 - 72)(183 - 224.375)] + [(69 - 72)(201 - 224.375)] + [(70 - 72)(206 - 224.375)] + [(72 - 72)(220 - 224.375)] + [(74 - 72)(226 - 224.375)] + [(74 - 72)(240 - 224.375)] + [(78 - 72)(253 - 224.375)] + [(79 - 72)(255 - 224.375)] = -5280

Σ((x - mean(x))^2) = [(67 - 72)^2] + [(69 - 72)^2] + [(70 - 72)^2] + [(72 - 72)^2] + [(74 - 72)^2] + [(74 - 72)^2] + [(78 - 72)^2] + [(79 - 72)^2] = 136

Using these values in the formulas:

m = -5280 / 136 ≈ -38.824
b = 224.375 - (-38.824 * 72) ≈ 2598.25

So the equation of the line is y = -38.824x + 2598.25.

Now, we can substitute x = 84 into the equation to make the prediction:

y = -38.824(84) + 2598.25 ≈ 307.7 lb

Therefore, you would expect a basketball player with a height of 84 inches to weigh approximately 307.7 pounds. Therefore, the answer is 307.7 lb.